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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Solving the geodesic equations ： ウィキペディア英語版 Solving the geodesic equations Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics. Physically, these represent the paths of (usually ideal) particles with no proper acceleration, their motion satisfying the geodesic equations. Because the particles are subject to no four-acceleration, the geodesics generally represent the straightest path between two points in a curved spacetime. ==The geodesic equation== (詳細はRiemannian manifold $M$, the geodesic equation written in a coordinate chart with coordinates $x^a$ is: :$\backslash frac\; +\; \backslash Gamma^\_\backslash frac\backslash frac\; =\; 0$ where the coordinates ''x''''a''(''s'') are regarded as the coordinates of a curve γ(''s'') in $M$ and $\backslash Gamma^\_$ are the Christoffel symbols. The Christoffel symbols are functions of the metric and are given by: :$\backslash Gamma^a\_\; =\; \backslash frac\; g^\; \backslash left(\; g\_\; +\; g\_\; -\; g\_\; \backslash right)$ where the comma indicates a partial derivative with respect to the coordinates: :$g\_\; =\; \backslash frac\; \backslash frac\; \backslash frac$ and applying the Euler–Lagrange equation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Solving the geodesic equations」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.